Initial program 0.4
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
Initial simplification0.4
\[\leadsto \frac{{\left(\pi \cdot \left(n \cdot 2\right)\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}{\sqrt{k}}\]
Taylor expanded around inf 17.6
\[\leadsto \frac{\color{blue}{e^{\left(\frac{1}{2} - \frac{1}{2} \cdot k\right) \cdot \left(\log \left(2 \cdot \pi\right) - \log \left(\frac{1}{n}\right)\right)}}}{\sqrt{k}}\]
Simplified0.5
\[\leadsto \frac{\color{blue}{{\left(2 \cdot \pi\right)}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)} \cdot {n}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}}}{\sqrt{k}}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto \frac{{\left(2 \cdot \pi\right)}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)} \cdot {n}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}}{\color{blue}{1 \cdot \sqrt{k}}}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{{\left(2 \cdot \pi\right)}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}}{1} \cdot \frac{{n}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}}{\sqrt{k}}}\]
Simplified0.5
\[\leadsto \color{blue}{{\left(2 \cdot \pi\right)}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}} \cdot \frac{{n}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}}{\sqrt{k}}\]
- Using strategy
rm Applied unpow-prod-down0.4
\[\leadsto \color{blue}{\left({2}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)} \cdot {\pi}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}\right)} \cdot \frac{{n}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}}{\sqrt{k}}\]
Final simplification0.4
\[\leadsto \frac{{n}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}}{\sqrt{k}} \cdot \left({\pi}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)} \cdot {2}^{\left((\frac{-1}{2} \cdot k + \frac{1}{2})_*\right)}\right)\]
